International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 403-408
doi:10.1155/S0161171298000556

On new strengthened Hardy-Hilbert's inequality

Bicheng Yang1 and Lokenath Debnath2

1Department of Mathematics, Guangdong Education College, Guangdong, Guangzhou 510303, China
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA

Received 27 February 1997; Revised 8 September 1997

Copyright © 1998 Bicheng Yang and Lokenath Debnath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, a new inequality for the weight coefficient ω(q,n) in the form ω(q,n):=∑m=1∞1m+n(nm)1/q              <πsin(π/p)−12π1/p+n−1/q(q>1,1p+1q=1,n∈N) is proved. This is followed by a strengthened version ofthe Hardy-Hilbert inequality.